What is the integral of 1/(3t) ?

The integral of 1/(3t) is 1/3 ln|t|+C

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integral of 1/(3t)

\int \frac{1}{3 t} d t

\frac{1}{3} ln ∣ t ∣ + C

Solution steps

\int \frac{1}{3 t} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int \frac{1}{t} d t

Use the common integral:

\int \frac{1}{t} d t = ln (∣ t ∣)

= \frac{1}{3} ln ∣ t ∣

Add a constant to the solution

= \frac{1}{3} ln ∣ t ∣ + C

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